Answer
False.
Work Step by Step
Assume the range of $f(x)=\frac{1}{x}$ is all real numbers. Then there exists an $x$ such that $\frac{1}{x}=0$. However, there doesn't exist an $x$ such that $\frac{1}{x}=0$. Thus, $0$ isn't part of the range, meaning that the range isn't all real numbers. Therefore, the statement is false.
